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Tensor Networks

Module IN2388

This Module is offered by TUM Department of Informatics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

IN2388 is a semester module in English language at Bachelor’s level and Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology
  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Content, Learning Outcome and Preconditions


- Fundamentals and graphical representation of tensor networks
- Mathematical approximation theory
- Backpropagation through tensor network operations
- Simulating strongly correlated quantum systems and digital quantum computers
- Probability distribution sampling using tensor networks

Learning Outcome

After successful completion of this module, students are familiar with the mathematical formalism and graphical notation for tensor networks. They can assess and apply tensor network approaches for approximating high-dimensional data. They understand why tensor network methods are suitable for simulating strongly correlated quantum systems, and are familiar with corresponding algorithms.


• MA0901 Linear Algebra for Informatics
• MA0902 Analysis for Informatics
• IN0018 Discrete Probability Theory
• Knowledge about quantum mechanics or computing helpful (but not a formal prerequisite)

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VI 4 Tensor Networks (IN2388) Huang, Q. Mendl, C. Milbradt, R. Mon, 08:00–10:00, MI 00.08.038
Thu, 08:00–10:00, MI 00.13.009A

Learning and Teaching Methods

The whiteboard lectures convey the mathematical formalism and graphical representation of tensor network methods and algorithm in-depth. The accompanying exercises for individual study deepen the understanding of the topics explained in the lecture, and foster the creative application of the learnt techniques.


Whiteboard or digital tablet, slides


W. Hackbusch, S. Kühn: A new scheme for the tensor representation. J. Fourier Anal. Appl. 15, 706 (2009)

M. Espig, W. Hackbusch, S. Handschuh, R. Schneider: Optimization problems in contracted tensor networks. Comput. Visual Sci. 14, 271 (2011)

U. Schollwöck: The density-matrix renormalization group in the age of matrix product states. Annals of Physics 326, 96 (2011)

R. Orús: Tensor networks for complex quantum systems. Nature Reviews Physics 1, 538 (2019)

J. Haegeman, Ch. Lubich, I. Oseledets, B. Vandereycken, F. Verstraete: Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016)

L. Vanderstraeten, J. Haegeman, F. Verstraete: Tangent-space methods for uniform matrix product states. SciPost Phys. Lect. Notes 7 (2019)

H.-J. Liao, J.-G. Liu, L. Wang, T. Xiang: Differentiable programming tensor networks. Phys. Rev. X 9, 031041 (2019)

Module Exam

Description of exams and course work

The assessment is by means of a written exam of 90 minutes, or a 20 minute oral examination. Problems on the underlying approximation theory test whether students can apply the acquired knowledge and methods to a new domain. Problems related to the graphical representation may ask students to express an algorithm stated in matrix notation into a graphical form. The exam assesses the knowledge of tensor network methods for simulating quantum systems for example by asking them to tailor an algorithm for a given quantum Hamiltonian. Reaching a certain fraction of the maximum number of homework points can be rewarded by a grade step bonus (“eine Notenstufe”) in the evaluation of the exam. The exact details are timely announced at the beginning of the lecture.

Exam Repetition

There is a possibility to take the exam in the following semester.

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